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Dawn has been using two bank accounts to save money for a car. the difference between account 1 and account 2 is $100. if she uses 3/8 of account 1 and 7/8 of account 2, dawn will have a down payment of $2,000. solve the system of equations to find the total amount of money dawn has in each account. a – b = 100 a b = 2,000 dawn has $ in account 1 and $ in account 2.

2 Answers

6 votes

Answer:

Dawn has $1670 in account 1 and $1570 in account 2

Explanation:

Ed2020

User Rick Donohoe
by
8.1k points
4 votes

Answer

Dawn has $1670 in account 1 and $1570 in account 2

Explanation

Let
a be the amount of money in account 1

Let
b be the amount of money in account 2

We know from our problem that the difference between account 1 and account 2 is $100, so:


a-b=100 equation (1)

We also know that if she uses 3/8 of account 1 and 7/8 of account 2, dawn will have a down payment of $2,000, so:


(3)/(8) a+(7)/(8) b=2000 equation (2)

Now let's solve our system of equations (1) and (2) step by step:

Step 1. Solve for
a in equation (1)


a-b=100


a=100+b equation (3)

Step 2. Replace equation (3) in equation (2) and solve for
b


(3)/(8) (100+b)+(7)/(8) b=2000


37.5 +(3)/(8) b+(7)/(8) b=2000


(5)/(4) b=1962.5


b=1570 equation (4)

Step 3. Replace equation (4) in equation (3)


a=100+1570


a=1670

Dawn has $1670 in account 1 and $1570 in account 2

User Newmoney
by
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